Rachel J. Goldberg, Guideline Research/Atlanta, Inc., Duluth, GA

Size: px
Start display at page:

Download "Rachel J. Goldberg, Guideline Research/Atlanta, Inc., Duluth, GA"

Transcription

1 PROC FACTOR: How to Interpret the Output of a Real-World Example Rachel J. Goldberg, Guideline Research/Atlanta, Inc., Duluth, GA ABSTRACT THE METHOD This paper summarizes a real-world example of a factor analysis with a VARIMAX rotation utilizing the System s PROC FACTOR procedure. Each step you must undergo to perform a factor analysis is described -- from the initial programming code to the interpretation of the PROC FACTOR output. The paper begins by highlighting the major issues that you must consider when performing a factor analysis using the SAS System s PROC FACTOR. This is followed by an explanation of sample PROC FACTOR program code, and then a detailed discussion of how to interpret the PROC FACTOR output. The main focus of the paper is to help SAS software beginning and average skill level users learn how to interpret programming code and output from PROC FACTOR. Some knowledge of Statistics and/or Mathematics would be helpful in order to understand parts of the paper. All of the results discussed utilize Base SAS and software. INTRODUCTION Factor analysis can be performed for various reasons, such as: + Exploratory data analysis prior to further analysis + Broad explanation of the data + Testing hypothesized explanations of the data The SAS System s PROC FACTOR provides an efficient manner in which to perform a factor analysis, no matter what the specific interests are of the user. To glean meaningful results from a factor analysis, several issues need to be addressed before running PROC FACTOR, correct SAS software code for running PROC FACTOR has to be written, and proper interpretation of the output from PROC FACTOR must take place. This paper first will broadly discuss the issues that need to be considered before running PROC FACTOR. It is beyond the scope of this paper to discuss the detailed statistical and mathematical explanations for the different types of factor analysis. Thus, this paper provides only basic explanations and does not attempt to give the reader all of the information needed to make an educated decision about what type of factor analysis to perform. Following the preliminary analysis discussion, the paper will explain an example of a PROC FACTOR program code. Finally, the paper concludes with how to interpret the results of example PROC FACTOR output. The SAS System provides several options for the PROC FACTOR initial factoring method that is used for analysis, such as Alpha, Maximum-Likelihood, and Principal Components Analysis. Each of these initial factoring methods generates uncorrelated factors. Arguments exist supporting all of the different initial factoring methods available. In this paper, it is assumed that the objetilve during the initial factor analysis is to determine the minimum number of factors that will adequately account for the covariation among the larger number of analysis variables. This objective can be achieved by using any of the initial factoring methods. Therefore, the PROC FACTOR default was used, Principal Components Analysis, which is further discussed in the EXAMPLE PROC FACTOR PROGRAM section below. TO ROTATE, OR NOT TO ROTATE? It is generally considered that using a rotation in factor analysis will produce more interpretable results. If the factor analysis is being performed specifically to gain an explanation of what factors or groups exist in the data or to confirm hypothesized assumptions about the data, rotation can be especially helpful. Factor patterns can be rotated through two different ways: + Orthogonal rotations which retain uncorrelated factors + Oblique rotations which create correlated factors While arguments exist supporting both types of rotation methods, factor analysis which uses an orthogonal rotation often creates a solution that is easier to grasp and interpret than a solution obtained from an oblique rotation. The factor analysis example discussed in this paper is performed for exploratory data analysis purposes and to discover simplified factor or dimension descriptions that exist in the data. Therefore, one of the common orthogonal rotation methods, VARIMAX, is discussed in the EXAMPLE PROC FACTOR PROGRAM section below. PROC FACTOR EXAMPLE GOALS FOR RUNNING PROC FACTOR For the example included in this paper, the overall goals for running PROC FACTOR are the following: PRELIMINARY THE STEPS ANALYSIS As with any data analysis and interpretation, there are certain data cleaning procedures that should be performed prior to beginning an in-depth look at the data. The steps to consider prior to running PROC FACTOR include (but are not limited to) the following: + Verification that all data values are valid, + Removal of any data outliers, + Reduction of data to the relevant analysis variables, and + Decision about what type of factor analysis to perform. BACKGROUND Determine the minimum number of factors that can adequately account for the variance in the data, Find simpler, easier to interpret factors through rotating the factors, and Determine a meaningful interpretation of the factors that provides insight into the data for use with further analysis. The real-world example that is discussed is based on a factor analysis performed on data from a very large energy services company. The data that is analyzed is the customer and energy usage information that was available for a sub-population that is serviced by the energy services company. 1

2 EXAMPLE PROC FACTOR PROGRAM PROC FACTOR DATA= SAVE. EXAMP METHOD = PRINCIPAL SCREE MINEIGEN = ONFACTOR = 16 ROTATE = VARIMAX REORDER OUT= SAVE. EXAMPFAC; VAR X2 -- GAPLL; that simplifies the interpretation of the factors by maximizing the variances of the squared loadings for each factor, which are the columns of the factor pattern. REORDER This option reorders the output from the factor procedure, so the variables that explain the largest amount of the variance for factor one are printed in descending order down to those that explain the smallest amount of the variance for factor one. The remaining factors are printed in a similar manner. The options invoked in the above PROC FACTOR program are described below: DATA = data set This names the data set that contains the observations to be factored. OUT = data set This specifies that an output data set be created. This data set will contain all of the data from the original input data set and the new factor variables, which are called FACTORI, FACTOR2, etc. These new variables contain the estimated factor scores, which can be used in further statistical analysis. METHOD = method This specifies what type of method is to be used to extract the initial factors. As discussed earlier, the Principal Components Analysis (PCA) method (PRINCIPAL) was chosen for the initial factor extraction. The PCA method simply transforms the set of variables into another set of variables; that is, the data is summarized by means of a linear combination of the observed data, This transformation is performed because of the objective mentioned earliec to account for as much variation as possible in the data. With PCA, the first component or factor is defined in such a way that the Iergest amount of variance in the data is explained by the first component. The second component or factor that is identified explains the second most about the variance in the data AND is perpendicular (thus, uncorrelated) to the first component. The remaining components, or factors, are found in a similar manner. EXAMPLE PROC FACTOR OUTPUT EIGENVALUES OF THE CORRELATION MATRIX What exactly are eigenvalues? They are values that consolidate the data variance in a matrix (the eigenvalue) while providing the linear combination of variables (the eigenvector) to do it. PROC FACTOR was initially run by allowing all of the variables entered into the procedure to be possible factors. For exploratory data analysis purposes, this is a preferred way to run factor analysis, so that all of the eigenvalues can be analyzed. Based on this analysis, it is determined how many factors will be included in the final factoring program. Thus, in the example PROC FACTOR.- Droaram shown ear~er, NFACTOR = 16 was specified. SCREE This option requests that a scree plot of the eigenvalues be printed, which will be discussed in the EXAMPLE PROC FACTOR OUTPUT section. MINEIGEN = n This option specifies the smallest eigenvalue for which a factor is retained. In this example, O was selected, which retains factors with any eigenvalue. NFACTOR = n This option specifies the number of factors to be extracted from the data. The default value, if this option is not specified, is the number of variables in the data. In this example, 16 factors were specified to be extracted from the data. This number was selected by first running PROC FACTOR without the NFACTOR option and analyzing the eigenvalues and scree plot. Based on this eigenvalue and scree plot analysis, which will be discussed in more detail in the EXAMPLE PROC FACTOR OUTPUT section, 16 initial factors were kept. ROTATE = method This option invokes one of the rotation methods available. If no method is specified, the SAS default is to use no rotation. Therefore, if no rotation method is selected, the initial method that is selected will be the only method used during the factoring procedure. As discussed earlier, the above program specifies the VARIMAX orthogonal rotation method, VARIMAX rotation is a transformation EIGENVALUES OF THE CORRELATION MATRIX Eigenvalue Difference Proportion Cumulative The above eigenvalue chart is a small portion of the chart of the eigenvalues ftom the PROC FACTOR output. In the full eigenvalue chart in the PROC FACTOR OUTPUT, the sum of the eigenvalues is displayed, which equals the number of variables. As previously explained, for the example PROC FACTOR program in which NFACTOR = 16 was specified, 16 eigenvalues were output into the eigenvalue chart. For the eigenvalues displayed in the chart above, the DIFFERENCE between successive values, the PROPORTION of the variation represented, and the CUMULATIVE proportion of the variation represented is shown. Generally, eigenvalues of 1 or greater are accepted as explaining an adequate amount of the data variance. Thus, when analyzing the eigenvalue chart to determine how many factors to keep in the solution, eigenvalues that were greater than 1 were kept. As the sample output above shows, the last factor that had an eigenvalue greater than 1 is Factor 16. Hence, one reason to keep the first 16 factors for the remainder of the factor analysis. 2

3 SCREE PLOT OF EIGENVALUES Now, another way to determine how many factors should be kept in theremainder of theanalysis istoanalyze the SCREE PLOT. What is a SCREE PLOT? The SCREE PLOT simply displays the eigenvalues for each of the factors in a plot, from the first eigenvalue (the one that explains the most variance) to the last eigenvalue. On a scree plot produced by PROC FACTOR, if you draw a line that runs between each of the eigenvalues, you will see the slope level off as the amount of variance that is explained by each eigenvalue is less and less. Thus, the further down the slope you go, you will see that the eigenvalues are not that much different from each other. Where the line levels off is where the scree really shows in your data: that is, it is where the debris, or unnecessary information, collects. Also, where the lines levels off indicates the point of diminishing returns. It is this general area that should be analyzed to determine which eigenvalues are providing enough information to warrant inclusion in further analysis and which ones should be eliminated. It is worth noting that it is considered OK to have too many as opposed to too few factors included in exploratory factor analysis. FACTOR PATTERN The elements of the Factor Pattern reflect the unique variance each factor contributes to the variance of an observed variable. The reason factor analysis is not stopped after this initial factoring stage, without rotating the factors, is that the factors as they currently exist are not easily interpretable. In an ideal solution, the variables should load highly (have a high value that approaches 1) on just one factor each. INITIAL FACTOR PATTERN: PRINCIPAL COMPONENTS This output simply summarizes the amount of variance in the data that is explained by each factor. As you can see by looking at the above sample PROC FACTOR output, each of FACTORI 3 through FACTORI 6, only explains 1.1 or less of the variance, compared to FACTORI which explains If this data had been factored in another iteration, it may have been useful to eliminate the factors that are not explaining very much of the data variance. FINAL COMMUNALITY ESTIMATES The table of the final communality estimates simply shows the squared multiple correlations for predicting the variables from the estimated factors. It can be derived by taking the sum of squares of each row of the factor pattern, or a weighted sum of squares if variable weights have been used. This is the variance of the observed variables that is accounted for by each factor. ROTATED FACTOR PATTERN Because a rotated factor analysis was specified, another factor pattern was output. As stated earlier, the VARIMAX rotation method was selected since it is considered to produce the most easily interpreted results. Thus, by rotating the factor pattern, a better explanation of the data should be gained. ROTATION METHOD: VARIMAX ROTATED FACTOR PATTERN FACTORI FACTOR2 FACTOR3 FACTOR4 X FACTOR PATTERN FACTORI FACTOR2 FACTOR3 FACTOR4 < K To determine whether or not the rotation made interpretation easier, look again at variable X33. As the sample PROC FACTOR output above shows, variable X33 now loads on FACTORI as -0.1 and loads on FACTOR2 as 0.8. This is much closer to the ideal solution in which each variable loads high (approaching a value of 1) on only one factor. In the above example, a sample of the PROC FACTOR output, look at variable X33. This variable has a loading of (a moderate loading) in Factor 1 and a loading of (a moderately to high loading) in Factor 2. Ideally, this variable would have a moderately high to high loading in only one factor, which would make it easily interpretable. Because many variables loaded in a similar manner as X33, the factor pattern was rotated, using the VARIMAX rotation method. ROTATION METHOD: VARIMAX FACTORI...FACTORI 3 FACTOR14 FACTORI 5 FACTOR INITIAL FACTOR METHOD: PRINCIPAL COMPONENTS FACTORI...FACTOR13 FACTOR14 FACTOR15 FACTOR As the above sample PROC FACTOR output shows, while the lower factors (15 & 16) explain more of the variance than prior to rotating the factors, they still do not provide much of an explanation. However, FACTORI 3 now explains 1.5 of the variance compared to just 1.1 prior to factor rotation. As previously stated, if this data had been factored in another iteration, it may have been useful to eliminate the factors that are not explaining very much of the data variance. 3

4 FINAL COMMUNALITY ESTIMATES The final communality estimates have not changed since the factors were rotated. This is because rotating the factors does not affect how much covariance is explained; it simply produces more interpretable results. STANDARDIZED SCORING COEFFICIENTS If one of the goals in performing factor analysis was to find factors to use in subsequent analyses, the estimated values of the factors, which are the factor scores, would need to be produced. In this paper s energy services example, since an output data set was requested, the standardized scoring coefficients are automatically printed. Generally, the individual variables factor scores are not used, the scores are used as a whole to represent the factor. INTERPRETATION OF PROC FACTOR OUTPUT NEXT STEPS From the PROC FACTOR output given directly from the SAS System, several things can be done, such as: + Using the factor scores in subsequent data analyses + Analyzing the factors to determine if each factor describes a particular dimension in the data + Determining if a preliminary hypothesis about the data is correct 0 Eliminating variables that do not load highly in any factor, which reduces redundancy in the data and unnecessary information In this paper s energy services example, as is often the case in the real-world, the next steps involved more than one of the above items. First, the factors were analyzed to determine what unique dimensions existed in the data. Second, the factor scores were used in subsequent analyses, such as with the SAS System s PROC FASTCLUS and PROC DISCRIM. The remainder of this paper will focus on the first use of this example PROC FACTOR output, creating a description of the dimensions in the energy services data. DESCRIBING THE FACTORS It is necessary to describe the 16 factors to ensure that insight has been gained into the dimensions in the energy services data. To create a description of each factor, the highest loading variables on each of the rotated factors are summarized, as shown in the Factor Summary Table that follows in the next column. As the Factor Summary Table shows, in some of the factors, only one variable had a reasonably high loading. Many researchers believe that at least two variables are necessary to validly explain a factor (load highly). For exploratory factor analysis, just trying to gain an understanding of the data, it has been argued that one variable can adequately explain a factor. Also, some of the factors in the above example only have a moderate to moderately high loading, such as FACTORI 5 s loading of 0.5. Because of some weaker factor loadings and the minimal amount of variance explained by some of the factors, as previously discussed, the current factors would need to be further analyzed and refined before taking the factor scores that were generated from this run of the PROC FACTOR program into subsequent SAS software procedures. FACTOR SUMMARY TABLE FACTORS VARS gapgg.9 gapkk.9 gapjj.9 gapff.9 gapee.9 gaphh.8 gapii.8 ~apdd.8 x33.9 X31.8 x34.8 X30.8 X29.8 X28.8 X32.8 x35.8 modx57 1 modx73.9 modx55.9 x54-1 modx86.8 modx85.8 Q K21.9 K K49.6 K K96.7 ( { K < < (13.7 (37.5.,.,-. However, for simple descriptive purposes, the current PROC FACTOR output is adequate. Hence, the meaning of each variable that loaded highly to moderately highly in the factors, as shown in the Factor Summary Table, is reviewed. Based on the variables definitions, descriptions of the 16 factors are surmised, as shown in the Factor Explanation Table on the next page. The factor explanations provide a general understanding of the unique dimensions that exist in the energy services data. These explanations can be used to: + Confirm/reject preliminary hypotheses about the data + Provide a first assessment of the dimensions/key issues in the data to be the focus of further analyses 4

5 FACTORS FACTOR EXPLANATION TABLE EXPLANATION 1 Expectations Gap 2 Importance of Service Issues 3 Customer Contact 4 Bill Services 5 No Modern Technology at Home 6 Presence of Modern Technology at Home 7 Customer Service 8 Community Services 9 Cost/Rates Issues 10 Number of People per Household 11 Power Quality Issues 12 Positive Service Perception 13 Negative Service Perception 14 Power Company Vs. Other Utilities 15 Prompt Service Call Response 16 Type of House CONCLUSIONS The example discussed in this paper provides the energy services company with initial dimensions in its data to further explore through more statistical analyses and by researching and confirming the findings. While factor analysis remains an imprecise science, the procedures discussed in this paper serve as a basic approach to discovering the unique factors that may exist in a set of data. To read more about the statistical and mathematical theories behind factor analysis and the other types of factor analysis, review the books listed in the references section of this paper. Good Luck and Happy Factoring! REFERENCES Johnson, Richard A. and Wichern, Dean W Applied Multivariafe Statistic/Analysis, Second Edifion. Englewood Cliffs, NJ: Prentice Hall. Kim, Jae-On and Mueller, Charles W /nfroducfion to Factor Analysis. What /s It and How to Do It. Sage University Paper Series on Quantitative Applications in the Social Sciences, series no Newbury Park, London, and New Delhi: Sage Publications. Given that a refined and final output was generated from this energy services data, the assumption can be made that these factors are describing the variance in the data. Thus, to learn more about why future changes in the data may occur, the issues that are described in the Factor Explanation Table can be scrutinized as the possible instigators of the change or variance. Kim, Jae-On and Mueller, Charles W Factor Analysis: Sfafisfica/ Methods and Practical Issues. Sage University Paper Series on Quantitative Applications in the Social Sciences, series no Newbury Park, London, and New Delhi: Sage Publications. SAS Institute Inc User s Guide, Volume f, ACECLUS-FREQ, Version 6, Fourth Edition. Cary, NC: SAS Institute Inc. VALIDATION OF FINDINGS There is no proven and universally accepted test that determines if the produced factoring solution is final or valid. However, in the attempt to validate the findings of a factor analyses, the results obtained from a factor analysis can be subjected to a series of informal tests like the ones listed below: ACKNOWLEDGMENTS SAS and SAS/STAT are registered trademarks or trademarks of SAS Institute Inc. in the USA and other indicates USA registration. + Perform another factor analysis using a different initial factor extraction method, instead of PCA, and then use a VARIMAX rotation + Perform another factor analysis using PCA for the initial factor extraction method, but then use a different type of rotation + Compare the results from the above two steps to the findings achieved through running PROC FACTOR with an initial factoring method of PCA with a VARIMAX rotation + Repeat the factor analyses performed in the above three steps using a different number of final factors + For data sets that are large enough, split the data in half and perform factor analysis on both sets of data, using the same initial extraction methods and rotation methods, and compare the two solutions AUTHORS ADDRESS The author may be contacted Rachel J. Goldberg Guideline Research/Atlanta, Inc Crestwood Parkway, N.W., Suite 520 Duluth, GA Phone: (770) Fax: (770) at 5

Overview of Factor Analysis

Overview of Factor Analysis Overview of Factor Analysis Jamie DeCoster Department of Psychology University of Alabama 348 Gordon Palmer Hall Box 870348 Tuscaloosa, AL 35487-0348 Phone: (205) 348-4431 Fax: (205) 348-8648 August 1,

More information

Introduction to Principal Components and FactorAnalysis

Introduction to Principal Components and FactorAnalysis Introduction to Principal Components and FactorAnalysis Multivariate Analysis often starts out with data involving a substantial number of correlated variables. Principal Component Analysis (PCA) is a

More information

PRINCIPAL COMPONENT ANALYSIS

PRINCIPAL COMPONENT ANALYSIS 1 Chapter 1 PRINCIPAL COMPONENT ANALYSIS Introduction: The Basics of Principal Component Analysis........................... 2 A Variable Reduction Procedure.......................................... 2

More information

Common factor analysis

Common factor analysis Common factor analysis This is what people generally mean when they say "factor analysis" This family of techniques uses an estimate of common variance among the original variables to generate the factor

More information

4. There are no dependent variables specified... Instead, the model is: VAR 1. Or, in terms of basic measurement theory, we could model it as:

4. There are no dependent variables specified... Instead, the model is: VAR 1. Or, in terms of basic measurement theory, we could model it as: 1 Neuendorf Factor Analysis Assumptions: 1. Metric (interval/ratio) data 2. Linearity (in the relationships among the variables--factors are linear constructions of the set of variables; the critical source

More information

FACTOR ANALYSIS. Factor Analysis is similar to PCA in that it is a technique for studying the interrelationships among variables.

FACTOR ANALYSIS. Factor Analysis is similar to PCA in that it is a technique for studying the interrelationships among variables. FACTOR ANALYSIS Introduction Factor Analysis is similar to PCA in that it is a technique for studying the interrelationships among variables Both methods differ from regression in that they don t have

More information

Getting Started in Factor Analysis (using Stata 10) (ver. 1.5)

Getting Started in Factor Analysis (using Stata 10) (ver. 1.5) Getting Started in Factor Analysis (using Stata 10) (ver. 1.5) Oscar Torres-Reyna Data Consultant otorres@princeton.edu http://dss.princeton.edu/training/ Factor analysis is used mostly for data reduction

More information

Exploratory Factor Analysis

Exploratory Factor Analysis Introduction Principal components: explain many variables using few new variables. Not many assumptions attached. Exploratory Factor Analysis Exploratory factor analysis: similar idea, but based on model.

More information

A Brief Introduction to Factor Analysis

A Brief Introduction to Factor Analysis 1. Introduction A Brief Introduction to Factor Analysis Factor analysis attempts to represent a set of observed variables X 1, X 2. X n in terms of a number of 'common' factors plus a factor which is unique

More information

Exploratory Factor Analysis Brian Habing - University of South Carolina - October 15, 2003

Exploratory Factor Analysis Brian Habing - University of South Carolina - October 15, 2003 Exploratory Factor Analysis Brian Habing - University of South Carolina - October 15, 2003 FA is not worth the time necessary to understand it and carry it out. -Hills, 1977 Factor analysis should not

More information

To do a factor analysis, we need to select an extraction method and a rotation method. Hit the Extraction button to specify your extraction method.

To do a factor analysis, we need to select an extraction method and a rotation method. Hit the Extraction button to specify your extraction method. Factor Analysis in SPSS To conduct a Factor Analysis, start from the Analyze menu. This procedure is intended to reduce the complexity in a set of data, so we choose Data Reduction from the menu. And the

More information

Factor Analysis. Advanced Financial Accounting II Åbo Akademi School of Business

Factor Analysis. Advanced Financial Accounting II Åbo Akademi School of Business Factor Analysis Advanced Financial Accounting II Åbo Akademi School of Business Factor analysis A statistical method used to describe variability among observed variables in terms of fewer unobserved variables

More information

Principal Component Analysis

Principal Component Analysis Principal Component Analysis ERS70D George Fernandez INTRODUCTION Analysis of multivariate data plays a key role in data analysis. Multivariate data consists of many different attributes or variables recorded

More information

Doing Quantitative Research 26E02900, 6 ECTS Lecture 2: Measurement Scales. Olli-Pekka Kauppila Rilana Riikkinen

Doing Quantitative Research 26E02900, 6 ECTS Lecture 2: Measurement Scales. Olli-Pekka Kauppila Rilana Riikkinen Doing Quantitative Research 26E02900, 6 ECTS Lecture 2: Measurement Scales Olli-Pekka Kauppila Rilana Riikkinen Learning Objectives 1. Develop the ability to assess a quality of measurement instruments

More information

Statistics in Psychosocial Research Lecture 8 Factor Analysis I. Lecturer: Elizabeth Garrett-Mayer

Statistics in Psychosocial Research Lecture 8 Factor Analysis I. Lecturer: Elizabeth Garrett-Mayer This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike License. Your use of this material constitutes acceptance of that license and the conditions of use of materials on this

More information

Factor Analysis. Sample StatFolio: factor analysis.sgp

Factor Analysis. Sample StatFolio: factor analysis.sgp STATGRAPHICS Rev. 1/10/005 Factor Analysis Summary The Factor Analysis procedure is designed to extract m common factors from a set of p quantitative variables X. In many situations, a small number of

More information

Principal Components Analysis (PCA)

Principal Components Analysis (PCA) Principal Components Analysis (PCA) Janette Walde janette.walde@uibk.ac.at Department of Statistics University of Innsbruck Outline I Introduction Idea of PCA Principle of the Method Decomposing an Association

More information

Factor Analysis. Chapter 420. Introduction

Factor Analysis. Chapter 420. Introduction Chapter 420 Introduction (FA) is an exploratory technique applied to a set of observed variables that seeks to find underlying factors (subsets of variables) from which the observed variables were generated.

More information

Principal Component Analysis

Principal Component Analysis Principal Component Analysis Principle Component Analysis: A statistical technique used to examine the interrelations among a set of variables in order to identify the underlying structure of those variables.

More information

A Brief Introduction to SPSS Factor Analysis

A Brief Introduction to SPSS Factor Analysis A Brief Introduction to SPSS Factor Analysis SPSS has a procedure that conducts exploratory factor analysis. Before launching into a step by step example of how to use this procedure, it is recommended

More information

The Science and Art of Market Segmentation Using PROC FASTCLUS Mark E. Thompson, Forefront Economics Inc, Beaverton, Oregon

The Science and Art of Market Segmentation Using PROC FASTCLUS Mark E. Thompson, Forefront Economics Inc, Beaverton, Oregon The Science and Art of Market Segmentation Using PROC FASTCLUS Mark E. Thompson, Forefront Economics Inc, Beaverton, Oregon ABSTRACT Effective business development strategies often begin with market segmentation,

More information

2. Linearity (in relationships among the variables--factors are linear constructions of the set of variables) F 2 X 4 U 4

2. Linearity (in relationships among the variables--factors are linear constructions of the set of variables) F 2 X 4 U 4 1 Neuendorf Factor Analysis Assumptions: 1. Metric (interval/ratio) data. Linearity (in relationships among the variables--factors are linear constructions of the set of variables) 3. Univariate and multivariate

More information

Factor Analysis and Structural equation modelling

Factor Analysis and Structural equation modelling Factor Analysis and Structural equation modelling Herman Adèr Previously: Department Clinical Epidemiology and Biostatistics, VU University medical center, Amsterdam Stavanger July 4 13, 2006 Herman Adèr

More information

T-test & factor analysis

T-test & factor analysis Parametric tests T-test & factor analysis Better than non parametric tests Stringent assumptions More strings attached Assumes population distribution of sample is normal Major problem Alternatives Continue

More information

FACTOR ANALYSIS NASC

FACTOR ANALYSIS NASC FACTOR ANALYSIS NASC Factor Analysis A data reduction technique designed to represent a wide range of attributes on a smaller number of dimensions. Aim is to identify groups of variables which are relatively

More information

Multivariate Analysis (Slides 13)

Multivariate Analysis (Slides 13) Multivariate Analysis (Slides 13) The final topic we consider is Factor Analysis. A Factor Analysis is a mathematical approach for attempting to explain the correlation between a large set of variables

More information

PRINCIPAL COMPONENTS AND THE MAXIMUM LIKELIHOOD METHODS AS TOOLS TO ANALYZE LARGE DATA WITH A PSYCHOLOGICAL TESTING EXAMPLE

PRINCIPAL COMPONENTS AND THE MAXIMUM LIKELIHOOD METHODS AS TOOLS TO ANALYZE LARGE DATA WITH A PSYCHOLOGICAL TESTING EXAMPLE PRINCIPAL COMPONENTS AND THE MAXIMUM LIKELIHOOD METHODS AS TOOLS TO ANALYZE LARGE DATA WITH A PSYCHOLOGICAL TESTING EXAMPLE Markela Muca Llukan Puka Klodiana Bani Department of Mathematics, Faculty of

More information

Exploratory Factor Analysis of Demographic Characteristics of Antenatal Clinic Attendees and their Association with HIV Risk

Exploratory Factor Analysis of Demographic Characteristics of Antenatal Clinic Attendees and their Association with HIV Risk Doi:10.5901/mjss.2014.v5n20p303 Abstract Exploratory Factor Analysis of Demographic Characteristics of Antenatal Clinic Attendees and their Association with HIV Risk Wilbert Sibanda Philip D. Pretorius

More information

NCSS Statistical Software Principal Components Regression. In ordinary least squares, the regression coefficients are estimated using the formula ( )

NCSS Statistical Software Principal Components Regression. In ordinary least squares, the regression coefficients are estimated using the formula ( ) Chapter 340 Principal Components Regression Introduction is a technique for analyzing multiple regression data that suffer from multicollinearity. When multicollinearity occurs, least squares estimates

More information

STATISTICA Formula Guide: Logistic Regression. Table of Contents

STATISTICA Formula Guide: Logistic Regression. Table of Contents : Table of Contents... 1 Overview of Model... 1 Dispersion... 2 Parameterization... 3 Sigma-Restricted Model... 3 Overparameterized Model... 4 Reference Coding... 4 Model Summary (Summary Tab)... 5 Summary

More information

What Are Principal Components Analysis and Exploratory Factor Analysis?

What Are Principal Components Analysis and Exploratory Factor Analysis? Statistics Corner Questions and answers about language testing statistics: Principal components analysis and exploratory factor analysis Definitions, differences, and choices James Dean Brown University

More information

Dimensionality Reduction: Principal Components Analysis

Dimensionality Reduction: Principal Components Analysis Dimensionality Reduction: Principal Components Analysis In data mining one often encounters situations where there are a large number of variables in the database. In such situations it is very likely

More information

APPRAISAL OF FINANCIAL AND ADMINISTRATIVE FUNCTIONING OF PUNJAB TECHNICAL UNIVERSITY

APPRAISAL OF FINANCIAL AND ADMINISTRATIVE FUNCTIONING OF PUNJAB TECHNICAL UNIVERSITY APPRAISAL OF FINANCIAL AND ADMINISTRATIVE FUNCTIONING OF PUNJAB TECHNICAL UNIVERSITY In the previous chapters the budgets of the university have been analyzed using various techniques to understand the

More information

Chapter 7 Factor Analysis SPSS

Chapter 7 Factor Analysis SPSS Chapter 7 Factor Analysis SPSS Factor analysis attempts to identify underlying variables, or factors, that explain the pattern of correlations within a set of observed variables. Factor analysis is often

More information

Factor Rotations in Factor Analyses.

Factor Rotations in Factor Analyses. Factor Rotations in Factor Analyses. Hervé Abdi 1 The University of Texas at Dallas Introduction The different methods of factor analysis first extract a set a factors from a data set. These factors are

More information

Psychology 7291, Multivariate Analysis, Spring 2003. SAS PROC FACTOR: Suggestions on Use

Psychology 7291, Multivariate Analysis, Spring 2003. SAS PROC FACTOR: Suggestions on Use : Suggestions on Use Background: Factor analysis requires several arbitrary decisions. The choices you make are the options that you must insert in the following SAS statements: PROC FACTOR METHOD=????

More information

Factor Analysis Example: SAS program (in blue) and output (in black) interleaved with comments (in red)

Factor Analysis Example: SAS program (in blue) and output (in black) interleaved with comments (in red) Factor Analysis Example: SAS program (in blue) and output (in black) interleaved with comments (in red) The following DATA procedure is to read input data. This will create a SAS dataset named CORRMATR

More information

How to Get More Value from Your Survey Data

How to Get More Value from Your Survey Data Technical report How to Get More Value from Your Survey Data Discover four advanced analysis techniques that make survey research more effective Table of contents Introduction..............................................................2

More information

Review Jeopardy. Blue vs. Orange. Review Jeopardy

Review Jeopardy. Blue vs. Orange. Review Jeopardy Review Jeopardy Blue vs. Orange Review Jeopardy Jeopardy Round Lectures 0-3 Jeopardy Round $200 How could I measure how far apart (i.e. how different) two observations, y 1 and y 2, are from each other?

More information

Assessment of Online Learning Environments: Using the OCLES(20) with Graduate Level Online Classes

Assessment of Online Learning Environments: Using the OCLES(20) with Graduate Level Online Classes www.ncolr.org/jiol Volume 7, Number 3, Winter 2008 ISSN: 15414914 Assessment of Online Learning Environments: Using the OCLES(20) with Graduate Level Online Classes Thomas A. DeVaney Nan B. Adams Cynthia

More information

Factor Analysis. Principal components factor analysis. Use of extracted factors in multivariate dependency models

Factor Analysis. Principal components factor analysis. Use of extracted factors in multivariate dependency models Factor Analysis Principal components factor analysis Use of extracted factors in multivariate dependency models 2 KEY CONCEPTS ***** Factor Analysis Interdependency technique Assumptions of factor analysis

More information

9.2 User s Guide SAS/STAT. The FACTOR Procedure. (Book Excerpt) SAS Documentation

9.2 User s Guide SAS/STAT. The FACTOR Procedure. (Book Excerpt) SAS Documentation SAS/STAT 9.2 User s Guide The FACTOR Procedure (Book Excerpt) SAS Documentation This document is an individual chapter from SAS/STAT 9.2 User s Guide. The correct bibliographic citation for the complete

More information

FACTOR ANALYSIS EXPLORATORY APPROACHES. Kristofer Årestedt

FACTOR ANALYSIS EXPLORATORY APPROACHES. Kristofer Årestedt FACTOR ANALYSIS EXPLORATORY APPROACHES Kristofer Årestedt 2013-04-28 UNIDIMENSIONALITY Unidimensionality imply that a set of items forming an instrument measure one thing in common Unidimensionality is

More information

Data analysis process

Data analysis process Data analysis process Data collection and preparation Collect data Prepare codebook Set up structure of data Enter data Screen data for errors Exploration of data Descriptive Statistics Graphs Analysis

More information

SAS Software to Fit the Generalized Linear Model

SAS Software to Fit the Generalized Linear Model SAS Software to Fit the Generalized Linear Model Gordon Johnston, SAS Institute Inc., Cary, NC Abstract In recent years, the class of generalized linear models has gained popularity as a statistical modeling

More information

Multivariate Analysis (Slides 4)

Multivariate Analysis (Slides 4) Multivariate Analysis (Slides 4) In today s class we examine examples of principal components analysis. We shall consider a difficulty in applying the analysis and consider a method for resolving this.

More information

5.2 Customers Types for Grocery Shopping Scenario

5.2 Customers Types for Grocery Shopping Scenario ------------------------------------------------------------------------------------------------------- CHAPTER 5: RESULTS AND ANALYSIS -------------------------------------------------------------------------------------------------------

More information

BEHAVIOR BASED CREDIT CARD FRAUD DETECTION USING SUPPORT VECTOR MACHINES

BEHAVIOR BASED CREDIT CARD FRAUD DETECTION USING SUPPORT VECTOR MACHINES BEHAVIOR BASED CREDIT CARD FRAUD DETECTION USING SUPPORT VECTOR MACHINES 123 CHAPTER 7 BEHAVIOR BASED CREDIT CARD FRAUD DETECTION USING SUPPORT VECTOR MACHINES 7.1 Introduction Even though using SVM presents

More information

Multivariate Analysis

Multivariate Analysis Table Of Contents Multivariate Analysis... 1 Overview... 1 Principal Components... 2 Factor Analysis... 5 Cluster Observations... 12 Cluster Variables... 17 Cluster K-Means... 20 Discriminant Analysis...

More information

DATA ANALYSIS AND INTERPRETATION OF EMPLOYEES PERSPECTIVES ON HIGH ATTRITION

DATA ANALYSIS AND INTERPRETATION OF EMPLOYEES PERSPECTIVES ON HIGH ATTRITION DATA ANALYSIS AND INTERPRETATION OF EMPLOYEES PERSPECTIVES ON HIGH ATTRITION Analysis is the key element of any research as it is the reliable way to test the hypotheses framed by the investigator. This

More information

Factor Analysis. Factor Analysis

Factor Analysis. Factor Analysis Factor Analysis Principal Components Analysis, e.g. of stock price movements, sometimes suggests that several variables may be responding to a small number of underlying forces. In the factor model, we

More information

Improving the Performance of Data Mining Models with Data Preparation Using SAS Enterprise Miner Ricardo Galante, SAS Institute Brasil, São Paulo, SP

Improving the Performance of Data Mining Models with Data Preparation Using SAS Enterprise Miner Ricardo Galante, SAS Institute Brasil, São Paulo, SP Improving the Performance of Data Mining Models with Data Preparation Using SAS Enterprise Miner Ricardo Galante, SAS Institute Brasil, São Paulo, SP ABSTRACT In data mining modelling, data preparation

More information

Exploratory Factor Analysis and Principal Components. Pekka Malo & Anton Frantsev 30E00500 Quantitative Empirical Research Spring 2016

Exploratory Factor Analysis and Principal Components. Pekka Malo & Anton Frantsev 30E00500 Quantitative Empirical Research Spring 2016 and Principal Components Pekka Malo & Anton Frantsev 30E00500 Quantitative Empirical Research Spring 2016 Agenda Brief History and Introductory Example Factor Model Factor Equation Estimation of Loadings

More information

Using Principal Components Analysis in Program Evaluation: Some Practical Considerations

Using Principal Components Analysis in Program Evaluation: Some Practical Considerations http://evaluation.wmich.edu/jmde/ Articles Using Principal Components Analysis in Program Evaluation: Some Practical Considerations J. Thomas Kellow Assistant Professor of Research and Statistics Mercer

More information

STA 4107/5107. Chapter 3

STA 4107/5107. Chapter 3 STA 4107/5107 Chapter 3 Factor Analysis 1 Key Terms Please review and learn these terms. 2 What is Factor Analysis? Factor analysis is an interdependence technique (see chapter 1) that primarily uses metric

More information

Applying Customer Attitudinal Segmentation to Improve Marketing Campaigns Wenhong Wang, Deluxe Corporation Mark Antiel, Deluxe Corporation

Applying Customer Attitudinal Segmentation to Improve Marketing Campaigns Wenhong Wang, Deluxe Corporation Mark Antiel, Deluxe Corporation Applying Customer Attitudinal Segmentation to Improve Marketing Campaigns Wenhong Wang, Deluxe Corporation Mark Antiel, Deluxe Corporation ABSTRACT Customer segmentation is fundamental for successful marketing

More information

RISK ANALYSIS ON THE LEASING MARKET

RISK ANALYSIS ON THE LEASING MARKET The Academy of Economic Studies Master DAFI RISK ANALYSIS ON THE LEASING MARKET Coordinator: Prof.Dr. Radu Radut Student: Carla Biclesanu Bucharest, 2008 Table of contents Introduction Chapter I Financial

More information

Data Analysis Tools. Tools for Summarizing Data

Data Analysis Tools. Tools for Summarizing Data Data Analysis Tools This section of the notes is meant to introduce you to many of the tools that are provided by Excel under the Tools/Data Analysis menu item. If your computer does not have that tool

More information

CHAPTER 8 FACTOR EXTRACTION BY MATRIX FACTORING TECHNIQUES. From Exploratory Factor Analysis Ledyard R Tucker and Robert C.

CHAPTER 8 FACTOR EXTRACTION BY MATRIX FACTORING TECHNIQUES. From Exploratory Factor Analysis Ledyard R Tucker and Robert C. CHAPTER 8 FACTOR EXTRACTION BY MATRIX FACTORING TECHNIQUES From Exploratory Factor Analysis Ledyard R Tucker and Robert C MacCallum 1997 180 CHAPTER 8 FACTOR EXTRACTION BY MATRIX FACTORING TECHNIQUES In

More information

Statistics for Business Decision Making

Statistics for Business Decision Making Statistics for Business Decision Making Faculty of Economics University of Siena 1 / 62 You should be able to: ˆ Summarize and uncover any patterns in a set of multivariate data using the (FM) ˆ Apply

More information

Topic 10: Factor Analysis

Topic 10: Factor Analysis Topic 10: Factor Analysis Introduction Factor analysis is a statistical method used to describe variability among observed variables in terms of a potentially lower number of unobserved variables called

More information

How to report the percentage of explained common variance in exploratory factor analysis

How to report the percentage of explained common variance in exploratory factor analysis UNIVERSITAT ROVIRA I VIRGILI How to report the percentage of explained common variance in exploratory factor analysis Tarragona 2013 Please reference this document as: Lorenzo-Seva, U. (2013). How to report

More information

Steven M. Ho!and. Department of Geology, University of Georgia, Athens, GA 30602-2501

Steven M. Ho!and. Department of Geology, University of Georgia, Athens, GA 30602-2501 PRINCIPAL COMPONENTS ANALYSIS (PCA) Steven M. Ho!and Department of Geology, University of Georgia, Athens, GA 30602-2501 May 2008 Introduction Suppose we had measured two variables, length and width, and

More information

SPSS ADVANCED ANALYSIS WENDIANN SETHI SPRING 2011

SPSS ADVANCED ANALYSIS WENDIANN SETHI SPRING 2011 SPSS ADVANCED ANALYSIS WENDIANN SETHI SPRING 2011 Statistical techniques to be covered Explore relationships among variables Correlation Regression/Multiple regression Logistic regression Factor analysis

More information

Component Ordering in Independent Component Analysis Based on Data Power

Component Ordering in Independent Component Analysis Based on Data Power Component Ordering in Independent Component Analysis Based on Data Power Anne Hendrikse Raymond Veldhuis University of Twente University of Twente Fac. EEMCS, Signals and Systems Group Fac. EEMCS, Signals

More information

Research Methodology: Tools

Research Methodology: Tools MSc Business Administration Research Methodology: Tools Applied Data Analysis (with SPSS) Lecture 02: Item Analysis / Scale Analysis / Factor Analysis February 2014 Prof. Dr. Jürg Schwarz Lic. phil. Heidi

More information

Factor Analysis Using SPSS

Factor Analysis Using SPSS Psychology 305 p. 1 Factor Analysis Using SPSS Overview For this computer assignment, you will conduct a series of principal factor analyses to examine the factor structure of a new instrument developed

More information

New SAS Procedures for Analysis of Sample Survey Data

New SAS Procedures for Analysis of Sample Survey Data New SAS Procedures for Analysis of Sample Survey Data Anthony An and Donna Watts, SAS Institute Inc, Cary, NC Abstract Researchers use sample surveys to obtain information on a wide variety of issues Many

More information

Factor analysis. Angela Montanari

Factor analysis. Angela Montanari Factor analysis Angela Montanari 1 Introduction Factor analysis is a statistical model that allows to explain the correlations between a large number of observed correlated variables through a small number

More information

Module 3: Correlation and Covariance

Module 3: Correlation and Covariance Using Statistical Data to Make Decisions Module 3: Correlation and Covariance Tom Ilvento Dr. Mugdim Pašiƒ University of Delaware Sarajevo Graduate School of Business O ften our interest in data analysis

More information

Practical Considerations for Using Exploratory Factor Analysis in Educational Research

Practical Considerations for Using Exploratory Factor Analysis in Educational Research A peer-reviewed electronic journal. Copyright is retained by the first or sole author, who grants right of first publication to the Practical Assessment, Research & Evaluation. Permission is granted to

More information

Mehtap Ergüven Abstract of Ph.D. Dissertation for the degree of PhD of Engineering in Informatics

Mehtap Ergüven Abstract of Ph.D. Dissertation for the degree of PhD of Engineering in Informatics INTERNATIONAL BLACK SEA UNIVERSITY COMPUTER TECHNOLOGIES AND ENGINEERING FACULTY ELABORATION OF AN ALGORITHM OF DETECTING TESTS DIMENSIONALITY Mehtap Ergüven Abstract of Ph.D. Dissertation for the degree

More information

Forecasting Geographic Data Michael Leonard and Renee Samy, SAS Institute Inc. Cary, NC, USA

Forecasting Geographic Data Michael Leonard and Renee Samy, SAS Institute Inc. Cary, NC, USA Forecasting Geographic Data Michael Leonard and Renee Samy, SAS Institute Inc. Cary, NC, USA Abstract Virtually all businesses collect and use data that are associated with geographic locations, whether

More information

Analyzing and interpreting data Evaluation resources from Wilder Research

Analyzing and interpreting data Evaluation resources from Wilder Research Wilder Research Analyzing and interpreting data Evaluation resources from Wilder Research Once data are collected, the next step is to analyze the data. A plan for analyzing your data should be developed

More information

Simple Predictive Analytics Curtis Seare

Simple Predictive Analytics Curtis Seare Using Excel to Solve Business Problems: Simple Predictive Analytics Curtis Seare Copyright: Vault Analytics July 2010 Contents Section I: Background Information Why use Predictive Analytics? How to use

More information

Introduction to Principal Component Analysis: Stock Market Values

Introduction to Principal Component Analysis: Stock Market Values Chapter 10 Introduction to Principal Component Analysis: Stock Market Values The combination of some data and an aching desire for an answer does not ensure that a reasonable answer can be extracted from

More information

Data Mining: An Overview of Methods and Technologies for Increasing Profits in Direct Marketing. C. Olivia Rud, VP, Fleet Bank

Data Mining: An Overview of Methods and Technologies for Increasing Profits in Direct Marketing. C. Olivia Rud, VP, Fleet Bank Data Mining: An Overview of Methods and Technologies for Increasing Profits in Direct Marketing C. Olivia Rud, VP, Fleet Bank ABSTRACT Data Mining is a new term for the common practice of searching through

More information

Effectiveness of Performance Appraisal: Its Outcomes and Detriments in Pakistani Organizations

Effectiveness of Performance Appraisal: Its Outcomes and Detriments in Pakistani Organizations Effectiveness of Performance Appraisal: Its Outcomes and Detriments in Pakistani Organizations Hafiz Muhammad Ishaq Federal Urdu University of Arts, Science and Technology, Islamabad, Pakistan E-mail:

More information

SUGI 29 Statistics and Data Analysis

SUGI 29 Statistics and Data Analysis Paper 205-29 Creating Scales from Questionnaires: PROC VARCLUS vs. Factor Analysis David J. Pasta, Ovation Research Group, San Francisco, CA Diana Suhr, University of Northern Colorado, Greeley, CO ABSTRACT

More information

USING SAS/STAT SOFTWARE'S REG PROCEDURE TO DEVELOP SALES TAX AUDIT SELECTION MODELS

USING SAS/STAT SOFTWARE'S REG PROCEDURE TO DEVELOP SALES TAX AUDIT SELECTION MODELS USING SAS/STAT SOFTWARE'S REG PROCEDURE TO DEVELOP SALES TAX AUDIT SELECTION MODELS Kirk L. Johnson, Tennessee Department of Revenue Richard W. Kulp, David Lipscomb College INTRODUCTION The Tennessee Department

More information

1. The standardised parameters are given below. Remember to use the population rather than sample standard deviation.

1. The standardised parameters are given below. Remember to use the population rather than sample standard deviation. Kapitel 5 5.1. 1. The standardised parameters are given below. Remember to use the population rather than sample standard deviation. The graph of cross-validated error versus component number is presented

More information

Didacticiel - Études de cas

Didacticiel - Études de cas 1 Topic Linear Discriminant Analysis Data Mining Tools Comparison (Tanagra, R, SAS and SPSS). Linear discriminant analysis is a popular method in domains of statistics, machine learning and pattern recognition.

More information

9.2 User s Guide SAS/STAT. Introduction. (Book Excerpt) SAS Documentation

9.2 User s Guide SAS/STAT. Introduction. (Book Excerpt) SAS Documentation SAS/STAT Introduction (Book Excerpt) 9.2 User s Guide SAS Documentation This document is an individual chapter from SAS/STAT 9.2 User s Guide. The correct bibliographic citation for the complete manual

More information

SAS Code to Select the Best Multiple Linear Regression Model for Multivariate Data Using Information Criteria

SAS Code to Select the Best Multiple Linear Regression Model for Multivariate Data Using Information Criteria Paper SA01_05 SAS Code to Select the Best Multiple Linear Regression Model for Multivariate Data Using Information Criteria Dennis J. Beal, Science Applications International Corporation, Oak Ridge, TN

More information

2. Simple Linear Regression

2. Simple Linear Regression Research methods - II 3 2. Simple Linear Regression Simple linear regression is a technique in parametric statistics that is commonly used for analyzing mean response of a variable Y which changes according

More information

Exploratory Factor Analysis

Exploratory Factor Analysis Exploratory Factor Analysis Definition Exploratory factor analysis (EFA) is a procedure for learning the extent to which k observed variables might measure m abstract variables, wherein m is less than

More information

The Effectiveness of Ethics Program among Malaysian Companies

The Effectiveness of Ethics Program among Malaysian Companies 2011 2 nd International Conference on Economics, Business and Management IPEDR vol.22 (2011) (2011) IACSIT Press, Singapore The Effectiveness of Ethics Program among Malaysian Companies Rabiatul Alawiyah

More information

What is Rotating in Exploratory Factor Analysis?

What is Rotating in Exploratory Factor Analysis? A peer-reviewed electronic journal. Copyright is retained by the first or sole author, who grants right of first publication to the Practical Assessment, Research & Evaluation. Permission is granted to

More information

Introduction to Matrix Algebra

Introduction to Matrix Algebra Psychology 7291: Multivariate Statistics (Carey) 8/27/98 Matrix Algebra - 1 Introduction to Matrix Algebra Definitions: A matrix is a collection of numbers ordered by rows and columns. It is customary

More information

Factor Analysis Using SPSS

Factor Analysis Using SPSS Factor Analysis Using SPSS The theory of factor analysis was described in your lecture, or read Field (2005) Chapter 15. Example Factor analysis is frequently used to develop questionnaires: after all

More information

The ith principal component (PC) is the line that follows the eigenvector associated with the ith largest eigenvalue.

The ith principal component (PC) is the line that follows the eigenvector associated with the ith largest eigenvalue. More Principal Components Summary Principal Components (PCs) are associated with the eigenvectors of either the covariance or correlation matrix of the data. The ith principal component (PC) is the line

More information

Statistical Models in R

Statistical Models in R Statistical Models in R Some Examples Steven Buechler Department of Mathematics 276B Hurley Hall; 1-6233 Fall, 2007 Outline Statistical Models Linear Models in R Regression Regression analysis is the appropriate

More information

THE USING FACTOR ANALYSIS METHOD IN PREDICTION OF BUSINESS FAILURE

THE USING FACTOR ANALYSIS METHOD IN PREDICTION OF BUSINESS FAILURE THE USING FACTOR ANALYSIS METHOD IN PREDICTION OF BUSINESS FAILURE Mary Violeta Petrescu Ph. D University of Craiova Faculty of Economics and Business Administration Craiova, Romania Abstract: : After

More information

A Comparison of Variable Selection Techniques for Credit Scoring

A Comparison of Variable Selection Techniques for Credit Scoring 1 A Comparison of Variable Selection Techniques for Credit Scoring K. Leung and F. Cheong and C. Cheong School of Business Information Technology, RMIT University, Melbourne, Victoria, Australia E-mail:

More information

Canonical Correlation

Canonical Correlation Chapter 400 Introduction Canonical correlation analysis is the study of the linear relations between two sets of variables. It is the multivariate extension of correlation analysis. Although we will present

More information

DISCRIMINANT FUNCTION ANALYSIS (DA)

DISCRIMINANT FUNCTION ANALYSIS (DA) DISCRIMINANT FUNCTION ANALYSIS (DA) John Poulsen and Aaron French Key words: assumptions, further reading, computations, standardized coefficents, structure matrix, tests of signficance Introduction Discriminant

More information

Understanding and Using Factor Scores: Considerations for the Applied Researcher

Understanding and Using Factor Scores: Considerations for the Applied Researcher A peer-reviewed electronic journal. Copyright is retained by the first or sole author, who grants right of first publication to the Practical Assessment, Research & Evaluation. Permission is granted to

More information

SIMPLIFIED PERFORMANCE MODEL FOR HYBRID WIND DIESEL SYSTEMS. J. F. MANWELL, J. G. McGOWAN and U. ABDULWAHID

SIMPLIFIED PERFORMANCE MODEL FOR HYBRID WIND DIESEL SYSTEMS. J. F. MANWELL, J. G. McGOWAN and U. ABDULWAHID SIMPLIFIED PERFORMANCE MODEL FOR HYBRID WIND DIESEL SYSTEMS J. F. MANWELL, J. G. McGOWAN and U. ABDULWAHID Renewable Energy Laboratory Department of Mechanical and Industrial Engineering University of

More information

Using SAS/INSIGHT Software as an Exploratory Data Mining Platform Robin Way, SAS Institute Inc., Portland, OR

Using SAS/INSIGHT Software as an Exploratory Data Mining Platform Robin Way, SAS Institute Inc., Portland, OR Using SAS/INSIGHT Software as an Exploratory Data Mining Platform Robin Way, SAS Institute Inc., Portland, OR ABSTRACT Data mining has captured the hearts and minds of business analysts seeking a solution

More information

Getting Correct Results from PROC REG

Getting Correct Results from PROC REG Getting Correct Results from PROC REG Nathaniel Derby, Statis Pro Data Analytics, Seattle, WA ABSTRACT PROC REG, SAS s implementation of linear regression, is often used to fit a line without checking

More information